Welcome to Econ 420 Applied Regression Analysis. Study Guide Week Nine. Some of you did not do as well as I expected on Assignment 2. So here is what we will do. I explain the assignment. You will redo Question 3 & 4 plus a couple of other questions.
This regression has fallen into the dummy variable trap. CFP and NOCFP have a perfect linear relationship because CFP + NOCFP = 1 no matter what. This violates the assumption that two independent variables cannot have a perfectly linear relationship. The regression cannot be estimated. One of the two dummy variables, probably NOCFP, should be left out of the regression.
a. Model ii is the best model. Model i has fallen into the dummy variable trap; one dummy variable must be omitted from the regression. Model iii does not have an intercept.
b. Looking at model ii, the hypothesis that the seasons of the year don’t affect EMPLOYMENT would be H0: B2=B3=B4=0. Use an F-test to test this null hypothesis versus the alternative hypothesis that at least one of the seasons matter. For the test, Model ii is the unrestricted model. The restricted model is EMPLOYMENT = B0 + B1GDP + e.
3. Use the data set dvd4 and EViews to test the hypothesis that at high levels of income people are less sensitive to the price of dvd than at low levels of income. Use 5 percent level of significance
a. H0: B1=B2, HA: B1 is not equal to B2
b. You will need to design your own F-test. The unrestricted model is:
c. After estimating the restricted and unrestricted models, you should get a residual sum of squares for the restricted model of 5.28 x 109 or 5,280,000,000. The residual sum of squares for the unrestricted model is 4.33 x 109 or 4,330,000,000. q, the number of restrictions, is 1. B1 can take any value, and then B2 must take the same value as B1 for the null hypothesis to be true, so B2 has a restricted value if the null hypothesis is true. The null hypothesis used here only imposes one restriction.
The critical value for F1,27 with a 1% error level is 7.68. Since the calculated value of the F-statistic is lower than the critical value, we cannot reject the null hypothesis that B1=B2. (Note that the critical value for a 5% error level is 4.21, so the null hypothesis could be rejected with a 5% error level).